The present invention relates to a circuit for the fast calculation of the discrete Fourier transform of a signal. It is used more particularly in the analysis of measuring signals, particularly in the analysis of the voltage supplied by a non-destructive eddy current testing probe.
It is known that this type of testing involves producing a variable magnetic field with the aid of a primary winding, subjecting a member to be tested to the field and sampling a voltage at the terminals of a secondary winding positioned in the vicinity of the tested member and analyzing this voltage. The primary and secondary windings are located in a probe, whose structure can be in different forms (they may coincide, be arranged in bridge-like manner, etc). Any defect in the tested member (change of size, variation of the electrical conductivity, variation of the magnetic permeability, cracks, etc) modifies the phase and intensity of the eddy currents induced in the member and correlatively changes the voltage sampled at the terminals of the probe.
When the member to be tested is magnetic, a special difficulty linked with the high permeability of material is encountered. This leads to the measuring signal being made dependent on certain parameters, such as the size, weight, etc.
In the case of the testing of magnetic members, the processing of the measuring signal essentially consists of the determination of its harmonics. In other words, it consists of a Fourier transformation. It has been shown that the knowledge of the harmonics of the signal makes it possible to obviate the aforementioned disadvantage with regard to the dependence of the measurement on certain parameters. Thus, the amplitude of the third harmonic, which reflects relatively well the structure of the part, but which remains sensitive to the weight thereof, can be weighted by the phase or amplitude of the fundamental term, which is a function of the weight of the part, in order to obtain a result which is substantially independent of the weight. Other combinations between harmonics make it possible to obtain freedom from other parameters. It is also known that the first harmonic component plays a predominant part. In an impedance plane, it can be represented by a point which, in the case of the passage of the member through a differential transducer, describes a figure eight curve, whose amplitude and orientation make it possible to determine defects of the tested member.
In a more general way, the circuit according to the invention is used at the output of a measuring device, like that illustrated in FIG. 1. A random measuring device 110 supplies an analog measuring signal at an output 111. A signal processing circuit 120 has an input 121 connected to output 111 and to output 122, which supplies information relative to the harmonics of the measuring signal. The preferred field of the invention is the non-destructive testing by eddy currents. In this case, device 110 comprises an alternating current generator 112, followed by an amplifier circuit 113 supplying a probe 114. The members to be tested 116 pass in the vicinity of probe 114. The measuring signal sampled by the probe is amplified by a circuit 118 and appears at output 111. It is this signal which is applied to the analysis circuit 120. A circuit 124 for processing the results can complete the analysis circuit in order to act on a sorting member 125 able, for example, to eject defective members.
The analysis circuit 120 performs a Fourier transformation of the signal applied to it. Although analog analysis circuits are possible, preference is now given to digital circuits, which make it possible to obtain a better accuracy and a greater flexibility of analysis. The signals to be processed are firstly converted into digital samples and then undergo the transformation in question. As this operation not takes place on a sequence of samples and not on a continuous quantity, it is conventionally called discrete Fourier transformation (DFT).
In block 120, FIG. 1 illustrates the block diagram of an analysis circuit of this type, which comprises an analog-digital converter 126, a random access memory 128, which will subsequently be referred to as an acquisition memory, which has a data input 129 connected to converter 126 and an output 131, a means 140 able to perform a discrete Fourier transformation on the samples contained in memory 128, said transformation making it possible to determine the real part R and the imaginary part I of the harmonics of the signal.
In order to provide a better understanding of the originality of the invention, it is necessary to give brief details on the discrete Fourier transformation.
It is a question of calculating a harmonic component X.sub.k, in which k is the rank of the harmonic in question from a sequence of samples x(n), in which n designates the rank of the sample in the sequence, whereby said rank ranges from 0 for the first sample to N-1for the last. The harmonics of rank k is given by the standard expression: ##EQU1## in which N designates the number of samples used for the calculation, the letter j being the symbol of the imaginary parts. By developing the exponential function, it becomes: ##EQU2## which makes it possible to separate the real part R.sub.k and imaginary part I.sub.k of the harmonic of rank k: ##EQU3##
The amplitude A and the phase .phi. of the harmonic in question can be gathered from the knowledge of R.sub.k and I.sub.k : ##EQU4##
The calculation of both R and I necessitate in each case N multiplicatons, because the N samples must be taken singly. It is therefore necessary to carry out 2N multiplications per harmonic. As it is possibile to calculate N harmonics with a sequence of N samples, a total discrete Fourier transformation consequently requires 2N.sup.2 multiplications.
It is obvious that this number becomes very large when N is high. For example, for 512 samples, it is equal to 524,288. Thus, the calculation time becomes prohibitive and the testing device cannot operate in real time.
It is for this reason that no fast eddy current testing device based on discrete Fourier transformation uses the calculating rules referred to hereinbefore, which constitute theoretical definitions of the quantities to be calculated rather than operating principles for the circuits used. High performance equipment uses more complicated algorithms intended to reduce the calculating time. The transformation performed is then called "fast" or fast Fourier transform (FFT).
The algorithms used are known and there is no need to refer to them here (COOLEY, SANDE and similar algorithms). It is merely pointed out that they involve factorizations of matrices using intermediate coefficients between the signal and its transform. Thus, calculation takes place in stages, the first starting with N samples and the last leading to N harmonic components. Thus, the number of operations performed in these algorithms is reduced and ranges from 2N.sup.2 to 2N log.sub.2 N. For N=512, this number is equal to 13,824, as compared with 524,288 on the basis of the previously defined rules.